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The evaluation of two-sided orthant probabilities for a quadrivariate normal distribution

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  • A. Hayter
  • Y. Lin

Abstract

In this paper it is shown how a general two-sided orthant probability for a quadrivariate normal distribution can be evaluated by a one-dimensional numerical integral calculation. The quadrivariate normal distribution can have any covariance matrix and any mean vector. This affords a practical and efficient method for the calculation of these probabilities which is superior to simulation methods. The implementation of the algorithm is discussed, and some examples of its performance are provided. Copyright Springer-Verlag 2012

Suggested Citation

  • A. Hayter & Y. Lin, 2012. "The evaluation of two-sided orthant probabilities for a quadrivariate normal distribution," Computational Statistics, Springer, vol. 27(3), pages 459-471, September.
    • Handle: RePEc:spr:compst:v:27:y:2012:i:3:p:459-471
    DOI: 10.1007/s00180-011-0267-z
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    References listed on IDEAS

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    1. Mark J. Schervish, 1984. "Multivariate Normal Probabilities with Error Bound," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(1), pages 81-94, March.
    2. Tetsuhisa Miwa & A. J. Hayter & Satoshi Kuriki, 2003. "The evaluation of general non‐centred orthant probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 223-234, February.
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    Cited by:

    1. Z. I. Botev, 2017. "The normal law under linear restrictions: simulation and estimation via minimax tilting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 125-148, January.

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